Download GPU Accelerated Simulation of Cardiac Activities

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JOURNAL OF COMPUTERS, VOL. 5, NO. 11, NOVEMBER 2010
GPU Accelerated Simulation of Cardiac
Activities
Rongdong Yu1,2, Yin Zhang1, and Sanyuan Zhang1*
1
College of Computer Science, Zhejiang University, Hangzhou, China, 310027
China Huadian Electric Power Research Institute, Hangzhou, China, 310030
Email: [email protected], [email protected], [email protected]
2
Patricia Chiang and Yiyu Cai
School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore, 639798
Email: [email protected], [email protected]
Jiangmin Zheng
School of Computer Engineering, Nanyang Technological University, Singapore, 639798
Email: [email protected]
Koon-Hou Mak
Mak Heart Clinic, Gleneagles Medical Centre, Singapore, 258499
Email: [email protected]
Abstract—Much efforts have been made to develop realistic
cardiac models for clinical and research purposes. However,
to implement these models always needs to handle excessive
computational loads due to the complex and dynamic
natures of the heart given limited computational power of
Central Processing Unit (CPU). In this paper, a real-time
approach to cardiac modeling is proposed based on the
Graphics Processing Unit (GPU). A hardware platform is
first designed and tested with a simplified model to
represent the cardiac activities. Motion of mesh-based heart
is then approximated to simulate the movement of each
vertex. Time functions are used within the GPU platform to
describe the cardiac cycle. The parallel computing feature of
GPU platform significantly speeds up the computation
process in real-time with over 140,000 vertices motion based
on the time functions. The program is developed on top of
CUDA architecture proposed and developed by nVIDIA.
Computational Experiments show visualization of the
cardiac dynamics is significantly benefiting from this new
solution. Further improvement of the GPU based cardiac
simulation is discussed.
Index Terms—GPGPU,
Simulation
I.
CUDA,
Cardiac
Activities,
INTRODUCTION
As a result of continued demand for programmability,
modern graphics processing units (GPUs) such as
nVIDIA’s GeForce 8 Series or later generations are
designed as programmable processors employing a large
number of processor cores[1]. The fast increasing power
of the GPU and its streaming architecture opens up a
range of new possibilities for a variety of applications.
*Corresponding Author
© 2010 ACADEMY PUBLISHER
doi:10.4304/jcp.5.11.1700-1705
With the enhanced programmability of GPUs, these chips
are now being capable of performing not only the specific
graphics computations they were originally designed for,
but also algorithms for non-graphics applications, such as
image
processing[3],
scientific
computing[2],
[4,5]
computational biology , Fast Fourier Transformation[6]
and so on. The evolution of GPUs is mainly driven by the
computer game market today. This leads to a relatively
low unit price and to very rapid developments of next
generation product. Most significantly, according to[7],
the growth rate of the number of transistors embedded in
GPUs is greater than for microprocessors and the peak
performance of GPUs is approximately ten times faster
than that of comparable CPUs.
However, there are still a number of challenges to be
solved in order to enable wider acceptance of the GPU
technologyby more users other than computer graphics
specialists. Restrictions of the underlying streaming
architecture have to be taken into account, e.g. random
access type of writes-to-memory is not supported and no
cross fragment data or persistent state is possible.
Currently, all the internal registers are flushed before a
new fragment is processed.
The two major GPU vendors, nVIDIA and AMD, just
proposed their new developing platforms: the Compute
Unified Device Architecture (CUDA) with nVIDIA[8] and
Stream with AMD[9]. Unlike previous GPU programming
models, these are proprietary approaches designed to
allow a direct access to their specific graphics hardware.
The vertex processor and fragment processor have
already become programmable. Actually, both of them
are designed as stream processors. This feature opens a
new field in GPU application, called general-purpose
JOURNAL OF COMPUTERS, VOL. 5, NO. 11, NOVEMBER 2010
computing on graphics processing units (GPGPU).
CUDA is an extension of the C programming language, it
treats the GPU as a data-parallel computing device
without the need of mapping computations to the
graphics pipeline; Stream is a virtual machine running
proprietary assembler code and Brook+ programming
language. Therefore, there is no compatibility concern
between the two platforms. Presently, even with Open
Computing Language (OpenCL), the so called
cross-platform solution, its code has to be converted into
one of the two platforms for compiling and running.
However, both platforms have to overcome some major
restrictions typically associated with previous GPGPU
approaches, e.g., those set by the traditional graphics
pipeline and the relative programming interfaces like
OpenGL and Direct3D.
A. Prior works
Study on cardiac physiology shows that pacemaker cells
in the heart generate action potentials at the beginning of
each cardiac cycle, which are conducted to the whole
heart through the conduction fibers spreading throughout
the myocardium[10]. The myocardial contractile cells are
then excited by the action potentials and contract
according to the sequence of excitations, and the heart
beats in a rhythmic motion. In order to properly model
the cyclic dynamics of the heart, computational methods
including many theoretical tools for the investigation of
cardiac physiology and pathology have been developed.
In the past two decades, many effective methods have
been introduced aiming to improve the simulation
accuracy of the electrical heart model. The cardiac
electric wave propagation model (E model)[11], the
electromechanical coupling model (EM model)[12], and
the biomechanical model (BM model)[13] are among the
most popular ones. Integration of these three models are
also proposed to give a more complete macroscopic
description of the physiological behavior of the heart;
usually referred as the cardiac physiome model[14]. To
simulate the heart cycle, the cardiac physiome model is
used by experiments and validated through different
criteria[12,15].
On the other hand, simplification strategy is often
adopted especially in the cardiac physiome modeling
where no closed form solution is given in order to
identify what may be neglected while still obtaining
acceptable results. For example, in the cardiac physiome
model, the continuous space of the heart has to be
discretized so that numerical methods can be applied to
solve the formulations. The finite element methods
(FEM) have been extensively used in computational
cardiology. Using tetrahedral elements[15], meshing
algorithm is relatively simple, yet the efficiency to
assemble system matrices is considerable.
B. Our works
We have built a simulating system for cardiac
intervention[16-18]. In our solution, boundary of heart
lumens are detected by utilizing voxel, catheter
deformation simulated by FEM method, is accelerated by
GPU pipeline based algorithms, and achieves real-time
© 2010 ACADEMY PUBLISHER
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performance. In this paper, algorithms based on GPU
have been implemented using C++ and CUDA and tested
on a tetrahedral mesh model consisting of vertices and
tetrahedrons. Expereiments show the GPU is capable for
high performance cardiac activities simulation.
II. METHODOLOGY
A. Anatomical Model
The mesh of the heart contains 148,516 vertices and
728,321 tetrahedrons[19]. The myocardium is represented
as a tetrahedral volumetric mesh including anatomical
information. The process to build such a model is detailed
in[20]. The main anatomical information we used is the
myocardium geometry, its division into different
anatomical parts, including details of valves and valve
gaps, see Fig. 1. Labeling of heart elements is done using
boundary index in vertices (see Table 1).
B. Myocardium Mechanical Model
The myocardium constitutive law is complex and
must include an active element for contraction, controlled
by the trans-membrane potential computed in the
previous section, and a passive element representing the
mechanical elasticity. Several constitutive laws have been
proposed in the literature[21- 26]. These laws are designed
to precisely fit rheological tests made on in vitro cardiac
muscle. Nash[12] has given a mechanical mathematic
model of the ventricle activities. This model is based on
the model generated from test of accurately anatomic
cardiac muscle. In Nash’s theory, the ventricular
mechanics model divides the entire cardiac cycle into
four phases, they are the diastolic filling, isovolumic
contraction, ejection and isovolumic relaxation phases.
During the cardiac cycle, the pressure of ventricle starts
from the rest stress of the non-load static state and
continuing increase in the cycle. Every state will be a
quasi-static state generated from the pre-existing state as
an initial state.
C. Simplified Mechanical Model
The ventricular mechanics model is efficient, but it has
to use the Newton’s method to minimize a system of
nonlinear residuals with respect to the set of unknown
solution variables. It is much complex, and no need for
every vertex of the model.
TABLE 1.
THE CORRESPONDENCE BETWEEN THE BOUNDARY SIGN AND
COMPONENTS.
Components
Color
Components
Color
interior
N.A.
pulmonary valve
red
mitral valve
red
right ventricle
blue
mitral valve
yellow
left ventricle
green
aortic valve
blue
valve of foramen oval
green
aortic valve
purple
valve of foramen oval
red
aortic valve
green
aorta
blue
right atrium
red
tricuspid valve
green
red
tricuspid valve
purple
right pulmonary v.
pulmonary valve
orange
tricuspid valve
pink
pulmonary valve
blue
right pulmonary a.
dark red
inferior vena cava
orange
outer surface
pink
left atrium
orange
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JOURNAL OF COMPUTERS, VOL. 5, NO. 11, NOVEMBER 2010
(A)
(B)
Figure 1. (A) The mesh of the heart model. (B) Points of the four
lumens surfaces, marked with different colors for different parts.
First, we give some time functions to represent the
relationship between location of the particles due to the
state theory of the ventricular mechanics model.
The entire cycle of ventricle and atrium could be
represented by a cosine equation,
S (t ) = 1 + n ⋅ cos (kt + φ )
(1)
with S(t) a zoom function by the time parameter t, k the
cycle controller coefficient, φ the initial phase, and n
the magnify coefficient.
Due to the normal heart cycle, for the motion
extended in different speed through parts, so we give the
particles of ventricle and atrium with different values of n
and φ .
To simulate the motion of the cardiac muscle, we get
the position limit hi of one particle i in the cardiac muscle
first, and particles within different lumens have their own
hi values. For one lumen, c represents the position of the
center of mass. The position of particle i at the time of t
can be expressed by
© 2010 ACADEMY PUBLISHER
xi = c + S (t )(hi − c )
(2)
where xi is the location of the particle i at the time t.
According to the algorithm the computational
complexity is O(N ) , it seems much fast, but for more
than 140,000 particles system, to compute so many
vertices’ coordinate is time-consuming. We find the
solution could been easily implemented in a parallel way,
naturally the best way to solve this problem is to use the
Single Instruction Multiple Data (SIMD) or Multiple
Instruction Multiple Data (MIMD) parallel machines with
dozens of processors and compute the position of each
particle apart.
All these approaches can be seen as accelerators - an
approach satisfying the demand for a low cost solution to
compute-intensive problems. The main advantage of
GPUs compared to the architectures mentioned above is
that they are commodity components.
D. CUDA Programming Model
In CUDA, the GPU is viewed as a compute device
suitable for parallel data applications. It has its own
device random access memory and may run a very high
number of threads in parallel. Threads are grouped in
blocks and many blocks may run in a grid of blocks. Such
structured sets of threads may be launched on a kernel of
code, possessing the data stored in the device memory.
Threads of the same block share data through fast shared
on-chip memory and can be synchronized through
synchronization points. Theoretically, having more active
threads per multiprocessor can help hide memory latency,
and can also better fill the instruction pipeline so there are
no idle processors. A multiprocessor is a set of stream
processors. In CUDA architecture, a multiprocessor
contains 8 individual stream processors. In the software
level, one block runs on one multiprocessor. According
to[27], the maximum number of threads that can run
concurrently on a multiprocessor is 1024 in the CUDA
architecture of version number later than 1.2. In practice,
the number of threads is further limited by the shared
on-chip memory and hence, the maximal number of
active
threads
per
multiprocessor
is
application-dependent.
In CUDA architecture as shown in Fig. 2, a
multiprocessor has on-chip memory of four types:
(1) One set of registers per processor,
(2) A parallel data cache or shared memory,
(3) A read-only constant cache,
(4) A read-only texture cache.
These on-chip memories are used to implement fast
I/O operations, especially, to speed up read and write
access to the non-cached device memory. Thus,
applications can take advantage of them by minimizing
over-fetch and roundtrips to the low bandwidth device
memory. Although the device memory has a low
bandwidth, it is big in size and shared by all
multiprocessors.
JOURNAL OF COMPUTERS, VOL. 5, NO. 11, NOVEMBER 2010
Figure 2.
Hardware architecture of CUDA based processors.
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Fig.ure 3. Threads and block assignment. In one block of first type
there are 512 threads, so for threads indices m and n, m*n=512, and
blocks index x, x=[N/512]+1, N is the total number of threads. In the last
block, y=N-(x-1)*512.
E. CUDA Based Simulation Algorithm Implementation
For the parallel applications many algorithms have
been proposed and implemented, because of too many
application-dependent
and
architecture-dependent
characters to consider. In this simulation algorithm,
computing of one particle position is implemented by one
thread, and we just put the particles to be processed in
one array, so the account of threads is equal to that of
particles N. These threads are distributed to the
multiprocessors, each processor is assigned a subset of
N/P (P is the number of processors) particles. For threads
assignment, we set number of threads per block to 512.
And there are [N/512]+1 blocks run on the device, where
N is not the multiple of 512. There are two types of
blocks. Blocks whose indices are from 0 to x-1, that
means the blocks from the first to the last but one, are of
the same type. They are 2D blocks, threads in the block
are in 2D grid, see in the Fig. 3. The last block is a special
one, because the total number of threads is not the
multiple of 512, which is the number of threads in the
first type of block. So the rests are put into the special 1D
block (0,x-1), threads here are assigned in an 1D queue,
see in the Fig. 3.
We simplified the threads and blocks assignment, let
m equal to 1, and n equal to 512. That means the first type
of blocks is simplified to 1D array, too. So the
management of threads and memory can be much easier,
but it has no improvement to the efficiency of the
algorithm, as shown in Fig. 4.
© 2010 ACADEMY PUBLISHER
Figure 4. Simplified threads and blocks assignment. All blocks are
treated as 1D array. And for blocks with index below x-1, all contain
512 threads. For block with index x-1, the threads number in it is y.
Data that shared by threads or keep using through
steps should be treated carefully, such as the data
describe the center of mass of four lumens and the
position limit of particles. The former should be shared
by threads; the latter should be used one at every time
step and kept no change. Both of the two kinds of data are
global existing, and shared by thread from different time
step at last, so it is not wise to put them in the registers,
though they are the fastest kind memory of lest amount.
A large number of particles lead these data to be put into
the global or the texture memory only. The share memory
can only share the data between processors in the same
multiprocessor, so it is not suitable, either, and global
memory without any cache leads threads to wait in long
access queue is also unsuitable. Finally, we choose the
texture memory to save the latter and the constant
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memory to save the former.
OpenGL is applied to visualize the result, and there
are functions in CUDA to map the particles into the
vertex array of GPU in the graphic memory that can also
be accessed and modified by Vertex Buffer Object (VBO)
technology, then GPU will draw them directly. And
different parts of the heart have been marked by different
colors as in Table 1.
III. PERFORMANCE EVALUATION
We have tested the solution by using CUDA Toolkit
2.0[8] and evaluated it on a workstation, having 1.866GHz
Intel E6300 processor, 2GB system memory and one
nVIDIA GeForce GTX 280 graphic card with 30
multiprocessors and 1GB graphic memory.
TABLE 2.
COMPARISON OF FPS (FRAME PER SECOND) AND SPEEDUP OF RUNNING
PERFORMANCE ON A GPU-ACCELERATED COMPUTING AND GPU
PIPELINE RENDER VERSION TO A CPU BASED COMPUTING AND
SOFTWARE RENDER VERSION BASED ON TRADITIONAL OPENGL
ARCHITECTURE.
Time
1
2
3
GPU-GPU
66.0
67.0
66.0
CPU-CPU
2.0
1.9
2.1
Acceleration
33.0x
35.3x
31.4x
components of our algorithms have been mapped onto the
GPU for execution. The CUDA architecture can not only
run as a high performance GPGPU platform but also
cooperate with other graphic libraries to accelerate the
animation displaying and computing physical effects.
In this work we just using a simplified physiologic
model to simulate the cardiac muscle activities, with the
GPU computing capability this simulation can be
real-time implemented. In the future, our work will
including the extension of the simulation algorithm, using
more complex model to improve the simulation accuracy
and validity.
ACKNOWLEDGMENT
The authors wish to thank Mr Chen Wenyu and Ms C
Indhumathi for their helping in the advices to the
implementation of the algorithm. This work was
supported by the National 973 program of China (No.
2009CB320804) and Zhejiang Provincial Natural Science
Foundation of China (Y1090597) and China Scholarship
Council.
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TABLE 3.
COMPARISON OF FPS (FRAME PER SECOND) AND SPEEDUP OF RUNNING
PERFORMANCE ON A GPU-ACCELERATED COMPUTING AND GPU
PIPELINE RENDER VERSION TO A CPU BASED COMPUTING AND GPU
PIPELINE RENDER VERSION.
Time
1
2
3
GPU-GPU
66.0
67.0
66.0
CPU-GPU
40.1
41.0
42.0
Acceleration
1.6x
1.6x
1.6x
[3]
[4]
[5]
From Table 2 we can see, our GPU implementation
achieves speedups of almost 33 compared to the CPU
based computing and software render version, and from
Table 3 we can see, our GPU implementation achieves
speedups of almost 1.6 compared to the CPU based
computing and GPU render version. Matrix convert and
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of CPU’s loading. Because of the number of processors,
the parallel processing performance of GPU is much
higher than it of CPU. And with the CPU based
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particle positions since this requires a transfer of vertex
attributes each frame. Visualization of the GPU pipeline
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cached in video memory.
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IV. CONCLUSION AND FUTURE WORK
The results of this work show that the new CUDA
compatible graphic cards are now advanced enough to be
considered as efficient hardware accelerators for the
cardiac activities simulation algorithm. All key
© 2010 ACADEMY PUBLISHER
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© 2010 ACADEMY PUBLISHER
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Rongdong Yu is a PhD student with
Zhejiang University, China. Sponsored by
the China Scholar Council, he is doing a
collaborative research with Nanyang
Technological
University
under
an
attachment project. His research interests
include Bio-medical Science and Computer
Sciences.
Dr. Yin Zhang, Associate Professor, she is
with the College of Computer Science,
Zhejiang University. Her research interests
are mainly in artificial intelligence,
geometric modeling and image processing.
Dr. Sanyuan Zhang is Professor with the
College of Computer Science, Zhejiang
University. His research interests are mainly
in computer aided geometric design, and
image processing.
Patricia Chiang receives her BEng degree
from National University of Singapore and
her
MSc
degree
from
Nanyang
Technological University. Her research
interests are in Signal Processing for
Biomedical Engineering applications.
Dr. Yiyu Cai is associate professor with the
School of Mechanical & Aerospace
Engineering,
Nanyang
Technological
University, Singapore. His research interests
include VR, Computational Biomedical
Sciences, and Interactive & Digital Media.
Dr. Jianmin Zheng is with the School of
Computer
Engineering,
Nanyang
Technological University. His research
interest includes computer aided geometric
design, CAD/CAM, computer graphics,
animation, digital imaging and visualization.
Dr. Koon-Hou MAK is an interventional
cardiologist and a visiting associate professor
with the School of Mechanial and Aerospace
Engineering,
Nanyang
Technological
University, Singapore. His research interest
is the development of medical devices,
interventional cardiology and acute coronary
syndromes.